You are interpreting “fundamental” as ‘highest priority’, which is not the only, (or most commonly expressed) definition of the word.

Fundamental is also defined as “so basic as to be hard to alter, resolve, or overcome.”

I would argue that ‘saving lives’ is not a ‘basic’ process; it is complex. However, informing someone’s next-of-kin of their passing, is a basic (ie fundamental) role of a healthcare facility.